Harmonia

This song uses the mathematics of Pythagorean tuning to unify its melody and rhythm.

Rhythm

Pythagorean tuning is based off of the 3:2 ratio. This table details how each degree in the scale is derived from the fundamental. Harmonia is in f.

minor second (gb) = 5(2/3) + 2(3) = 28/3 beats
minor sixth (db)= 4(2/3) + 2(3) = 26/3 beats
minor third (ab) = 3(2/3) + 2(2) = 6 beats
minor seventh (eb) = 2(2/3) + 2(2) = 16/3 beats
perfect fourth (bb) = 2/3 + 2 = 8/3 beats
unison (f) = 1 beat
perfect fifth (c) = 3/2 beats
major second (g) = 2(3/2) + 1/2 = 7/2 beats
major sixth (d) = 3(3/2) + 1/2 = 5 beats
major third (a) = 4(3/2) + 2(1/2) = 7 beats
major seventh (e) = 5(3/2) + 2(1/2) = 17/2 beats

Every e in this song is sounded for 17/2 beats. Every gb is held for 28/3 beats. Every d lasts for 5 beats. And so on.

Top Two Voices

The treble clef moves in seconds, while the bass moves in thirds.

Bottom Two Voices

The bottom two voices are drawn from the Gloria of the Missa De Angelis. The treble clef sings every second note. The bass plays every third note.

Lyrics

This hybrid Latin and Greek phrase has 3 + 2 = 5 parses even though it is very short.

Parse 1

γ = Greek emphasis particle
lum = Latin stem
εν = Greek preposition
animo = Latin noun

Parse 2

γ = Greek emphasis particle
lumεν = lumen = Latin noun
animo = Latin noun

Parse 3

γ = Greek emphasis particle
lum = Latin stem
εν = in = English prefix
animo = Latin noun

Parse 4

γ’lum = gloom = English noun
εν = in = English prefix
animo = Latin noun

Parse 5

γ’lum = gloom = English noun
εν = Greek preposition
animo = Latin noun

While these parses sometimes make little difference semantically, the fact that something so small has so many morphological interpretations is itself intriguing. The phrase is syntactically, but not semantically, beautiful.

The score, as well as all the python and lilypond code I used, can be found here.

posted by mxcollins